Properties

Label 729.1
Level 729
Weight 1
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 39366
Trace bound 0

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Defining parameters

Level: \( N \) = \( 729 = 3^{6} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(39366\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(729))\).

Total New Old
Modular forms 660 330 330
Cusp forms 12 6 6
Eisenstein series 648 324 324

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q + 3 q^{19} - 6 q^{28} + 3 q^{37} - 3 q^{64} - 6 q^{73} - 3 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(729))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
729.1.b \(\chi_{729}(728, \cdot)\) None 0 1
729.1.d \(\chi_{729}(242, \cdot)\) None 0 2
729.1.f \(\chi_{729}(80, \cdot)\) 729.1.f.a 6 6
729.1.h \(\chi_{729}(26, \cdot)\) None 0 18
729.1.j \(\chi_{729}(8, \cdot)\) None 0 54
729.1.l \(\chi_{729}(2, \cdot)\) None 0 162

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(729))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(729)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)